Sobolev Estimates for the Complex Monge-Ampère Operator on Complex Manifolds

Sobolev Estimates for the Complex Monge-Ampère Operator on Complex Manifolds

Abstract

Solutions of the complex Monge-Amp\`ere Equation are obtained in the Sobolev topology on complex manifolds and through the Delta-Delta-Bar Lemma, in case the manifold is compact K\"ahler, a simple proof is given of the Aubin-Calabi-Yau Theorem.